Simultaneous determination of multiple low-lying energy levels on a superconducting quantum processor

Determining the ground and low-lying excited states is critical in numerous scenarios. Recent work has proposed the ancilla-entangled variational quantum eigensolver (AEVQE) that utilizes entanglement between ancilla and physical qubits to simultaneously target multiple low-lying energy levels. In this work, we report the implementation of the AEVQE on a superconducting quantum cloud platform, demonstrating the full procedure of solving the low-lying energy levels of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mrow> <a:mi mathvariant="normal">H</a:mi> </a:mrow> </a:mrow> </a:math> <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msub> <d:mi/> <d:mn>2</d:mn> </d:msub> </d:math> molecule and the transverse-field Ising models (TFIMs). We obtain the potential energy curves of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mrow> <f:mrow> <f:mi mathvariant="normal">H</f:mi> </f:mrow> </f:mrow> </f:math> <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi/> <i:mn>2</i:mn> </i:msub> </i:math> and show an indication of the ferromagnetic to paramagnetic phase transition in the TFIMs from the average absolute magnetization. Moreover, we investigate multiple factors that affect the algorithmic performance and provide a comparison with ancilla-free VQE algorithms. Our work demonstrates the feasibility of the AEVQE algorithm and offers guidance for the VQE approach in solving realistic problems on publicly accessible quantum platforms.